Consider a generic power series: i. s(x) = 0 anxn n=0 Prove that if S converges...

 

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Consider a generic power series: i. s(x) = 0 anxn n=0 Prove that if S converges for some xo > 0, then it converges for any x₁ where |x₁|< Ixol. Likewise, if S diverges for some other x₂ > 0, then it diverges for any X3 > X2. Consider a generic power series: i. s(x) = 0 anxn n=0 Prove that if S converges for some xo > 0, then it converges for any x₁ where |x₁|< Ixol. Likewise, if S diverges for some other x₂ > 0, then it diverges for any X3 > X2.

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